The history of Morris Dance and Tunes is quite complex, but basically, the dancers had to dance to whatever their musician could play (or sing, if no musician was available). Most available dances are called by names of 17th/18th/19th century 'pop' songs, even though the dances may be older. Sometimes the names and tunes got swapped about, so Highland Mary (a song) could have been swapped to Country Gardens by one team, although others still used the original Higland Mary tune. There are at least a dozen versions of Constant Bill, Black Joke, Shepherds Hey.
Summary - you get dances of the same name to different tunes, and dances to the same tune with different names